CHAPTER 3
Decision Analysis
TRUE/FALSE
3.1
Expected Monetary Value (EMV) is the average or expected monetary outcome of a
decision if it can be repeated a large number of times.
ANSWER: TRUE
3.2
Expected Monetary Value (EMV) is the payoff you should expect to occur when you
choose a particular alternative.
ANSWER: FALSE
3.3
The decision maker has little or no control over a state of nature.
ANSWER: TRUE
3.4
Decision making under risk is a probabilistic decision situation.
ANSWER: TRUE
3.5
The difference in decision making under risk and decision making under uncertainty is that
under risk, we think we know the probabilities of the states of nature, while under
uncertainty we do not know the probabilities of the states of nature.
ANSWER: TRUE
3.6
EVPI (Expected Value of Perfect Information) is a measure of the maximum value of
additional information.
ANSWER: TRUE
3.7
When using the EOL as a decision criterion, the best decision is the alternative with the
least EOL value.
ANSWER: TRUE
3.8
To determine the effect of input changes on decision results, we should perform a
sensitivity analysis.
ANSWER: TRUE
3.9
The maximax decision criterion is used by pessimistic decision makers and maximizes the
maximum outcome for every alternative.
ANSWER: FALSE
3.10 The maximin decision criterion is used by pessimistic decision makers and minimizes the
maximum outcome for every alternative.
ANSWER: FALSE
38
Decision Analysis ● Chapter 3
3.11 Marginal analysis is an aid to decision making when there are a large number of
alternatives and/or states of nature.
ANSWER: TRUE
3.12 The decision theory processes of maximizing Expected Monetary Value and minimizing
Expected Opportunity Loss should lead us to choose the same alternatives.
ANSWER: TRUE
3.13 The several criteria (maximax, maximin, equally likely, criterion of realism, minimax) used
for decision making under uncertainty may lead to the choice of different alternatives.
ANSWER: TRUE
3.14 One advantage of using decision trees over decision tables when making sequential
decisions is that the tree better depicts the sequential aspect of the decisions.
ANSWER: TRUE
3.15 The nodes on decision trees represent either decisions or states of nature.
ANSWER: TRUE
3.16 Any problem that can be presented in a decision table can also be graphically portrayed in a
decision tree.
ANSWER: TRUE
3.17 Any problem that can be represented in a decision tree can be easily portrayed in a decision
table.
ANSWER: FALSE
3.18 The expected value of sample information (EVSI) is equal to the expected value of the best
decision with sample information (at no cost to gather) less the maximum expected
monetary value (EMV).
ANSWER: TRUE
3.19 The EMV approach and Utility theory always result in the same choice of alternatives.
ANSWER: FALSE
3.20 Utility theory may help the decision maker include the impact of qualitative factors that are
difficult to include in the EMV model.
ANSWER: TRUE
39
Decision Analysis ● Chapter 3
3.21 In a decision problem where we wish to use Bayes' theorem to calculate posterior
probabilities, we should always begin our analysis with the assumption that all states of
nature are equally likely, and use the sample information to revise these probabilities to
more realistic values.
ANSWER: FALSE
3.22 A utility curve that shows utility increasing at an increasing rate as the monetary value
increases represents the utility curve of a risk seeker.
ANSWER: TRUE
3.23 A utility curve that shows utility increasing at a decreasing rate as the monetary value
increases represents the utility curve of a risk seeker.
ANSWER: FALSE
3.24 If someone has a utility curve that increases linearly with increasing monetary value, we
would call this person risk indifferent or risk neutral.
ANSWER: TRUE
3.25 Utility values range from -1 to +1.
ANSWER: FALSE
3.26
By studying a person's Utility Curve, one can determine whether the individual is a risk
seeker, risk avoider, or is indifferent to risk.
ANSWER: TRUE
3.27
Rational people make decisions that maximize the expected utility.
ANSWER: TRUE
3.28
Utility theory provides a decision criterion that is superior to the EMV or EOL in that it
may allow the decision maker to incorporate her own attitudes toward risk
ANSWER: TRUE
3.29 The assignment of a utility value of 1 to an alternative implies that alternative is preferred
to all others.
ANSWER: TRUE
3.30 The assignment to a utility value of 0 to an alternative implies the alternative is preferred
to all others.
ANSWER: FALSE
40
Decision Analysis ● Chapter 3
3.31 The following figure illustrates a utility curve for someone who is a risk seeker.
ANSWER: TRUE
MULTIPLE CHOICE
3.32 Expected monetary value (EMV) is
(a) the average or expected monetary outcome of a decision if it can be repeated a large
number of times.
(b) the average or expected value of the decision, if you know what would happen ahead
of time.
(c) the average or expected value of information if it were completely accurate.
(d) the amount you would lose by not picking the best alternative.
(e) a decision criterion that places an equal weight on all states of nature.
ANSWER: a
3.33 A pessimistic decision making criterion is
(a)
(b)
(c)
(d)
(e)
maximax.
equally likely.
maximin.
decision making under certainty.
minimax.
ANSWER: c
3.34 Which of the following is true about the expected value of perfect information?
(a) It is the amount you would pay for any sample study.
(b) It is calculated as EMV minus EOL.
(c) It is calculated as expected value with perfect information minus maximum EMV.
(d) It is the amount charged for marketing research.
(e) none of the above
ANSWER: c
41
Decision Analysis ● Chapter 3
3.35 If product demand follows a normal distribution and we want to apply marginal analysis,
we need to know
(a)
(b)
(c)
(d)
(e)
the mean sales estimate.
the standard deviation of the sales estimate.
the marginal profit.
the marginal loss.
all of the above
ANSWER: e
3.36 The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
C
120
140
120
200
100
50
100
120
180
0
0
0
What decision would an optimist make?
(a)
(b)
(c)
(d)
(e)
Alternative 1
Alternative 2
Alternative 3
Do Nothing
none of the above
ANSWER: b
3.37 The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
C
120
140
120
200
100
50
100
120
180
0
0
0
What decision would a pessimist make?
(a)
(b)
(c)
(d)
(e)
Alternative 1
Alternative 2
Alternative 3
Do Nothing
none of the above
ANSWER: a
42
Decision Analysis ● Chapter 3
3.38 The following is an opportunity loss table.
Alternatives
Alternative 1
Alternative 2
Alternative 3
States of Nature
A
B
C
0
90
85
50
0
110
75
80
0
What decision should be made based on the minimax regret criterion?
(a)
(b)
(c)
(d)
(e)
Alternative 1
Alternative 2
Alternative 3
does not matter
none of the above
ANSWER: c
3.39 The following is an opportunity loss table.
Alternatives
Alternative 1
Alternative 2
Alternative 3
States of Nature
A
B
C
30
0
10
5
20
0
0
20
25
What decision should be made based on the minimax regret criterion?
(a)
(b)
(c)
(d)
(e)
Alternative 1
Alternative 2
Alternative 3
State of Nature C
none of the above
ANSWER: b
43
Decision Analysis ● Chapter 3
3.40 The following is an opportunity-loss table.
Alternatives
Alternative 1
Alternative 2
Alternative 3
State of Nature
A
B
C
20 100
0
100
0
25
0
40
90
The probabilities for the states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If
a person were to use the expected opportunity loss criterion, what decision would be
made?
(a)
(b)
(c)
(d)
(e)
Alternative 1
Alternative 2
Alternative 3
State of Nature C
none of the above
ANSWER: b
3.41 The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
C
100 120 180
120 140 120
200 100
50
0
0
0
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a
person selected Alternative 1, what would the expected profit be?
(a)
(b)
(c)
(d)
(e)
120
133.33
126
180
none of the above
ANSWER: c
44
Decision Analysis ● Chapter 3
3.42
Dr. Mac, a surgeon, must decide what mode of treatment to use on Mr. Samuels. There
are three modes of treatment, Mode A, B, and C; and three possible states of nature:
1.Treatment succeeds and patient leads a normal life, 2. Patient survives treatment but is
permanently disabled, and 3. Patient fails to survive treatment. Dr. Mac has prepared the
decision table below. What mode of treatment maximizes the expected value?
Treatment
Mode
Outcome
Normal Life
A
$1,000,000
P(outcome)
.5
B
$3,000,000
P(outcome)
.5
C
$10,000,000
P(outcome)
.4
(a)
(b)
(c)
(d)
(e)
Disability
-$2,000,000
.2
-$2,500,000
.3
-$5,000,000
.4
Non-Survival
-$500,000
.3
-$500,000
.2
-$600,000
.2
Mode A
Mode B
Mode C
All three treatments are equally desirable.
none of the above
ANSWER: c
3.43 Consider the following payoff table.
Alternatives
Alternative 1
Alternative 2
Probability
States of Nature
A
B
100
150
200
100
0.4
0.6
Based upon these probabilities, a person would select Alternative 2. Suppose there is
concern about the accuracy of these probabilities. It can be stated that Alternative 2 will
remain the best alternative as long as the probability of A is at least
(a)
(b)
(c)
(d)
(e)
0.33.
0.50.
0.40.
0.60.
none of the above
ANSWER: a
45
Decision Analysis ● Chapter 3
3.44 Consider the following payoff table.
Alternatives
Alternative 1
Alternative 2
Probability
States of Nature
A
B
100
150
200
100
0.4
0.6
How much should be paid for a perfect forecast of the state of nature?
(a)
(b)
(c)
(d)
(e)
170
30
10
100
none of the above
ANSWER: b
3.45 The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
C
100 120 180
200 100
50
120 140 120
0
0
0
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a
perfect forecast of the future were available, what is the expected value with this perfect
information?
(a) 130
(b) 160
(c) 166
(d) 36
(e) none of the above
ANSWER: c
46
Decision Analysis ● Chapter 3
3.46 The following is a payoff table giving profits for various situations.
Alternatives
Alternative 1
Alternative 2
Alternative 3
Do Nothing
States of Nature
A
B
C
100 120
180
200 100
50
120 140
120
0
0
0
The probabilities for states of nature A, B, and C are 0.3, 0.5, and 0.2, respectively. If a
perfect forecast of the future were available, what is the expected value of perfect
information (EVPI)?
(a)
(b)
(c)
(d)
(e)
166
0
36
40
none of the above
ANSWER: c
3.47 Nick has plans to open some pizza restaurants, but he is not sure how many to open. He
has prepared a payoff table to help analyze the situation.
Alternatives
Open 1
Open 2
Do Nothing
States of Nature
Good
Fair
Poor
Market
Market
Market
380,000
70,000 - 400,000
200,000
80,000 - 200,000
0
0
0
As Nick does not know how his product will be received, he assumes that all three states
of nature are equally likely to occur. If he uses the equally likely criterion, what decision
would he make?
(a)
(b)
(c)
(d)
(e)
open 1
open 2
good market
fair market
poor market
ANSWER: b
47
Decision Analysis ● Chapter 3
3.48 Nick has plans to open some pizza restaurants, but he is not sure how many to open. He
has prepared a payoff table to help analyze the situation.
Alternatives
Open 1
Open 2
Do Nothing
States of Nature
Good
Fair
Poor
Market
Market
Market
380,000
70,000
-400,000
200,000
80,000
-200,000
0
0
0
Nick believes there is a 40 percent chance that the market will be good, a 30 percent
chance that it will be fair, and a 30 percent chance that it will be poor. A market research
firm will analyze market conditions and will provide a perfect forecast (they provide a
money back guarantee). What is the most that should be paid for this forecast?
(a)
(b)
(c)
(d)
(e)
$ 44,000
$ 53,000
$123,000
$176,000
none of the above
ANSWER: c
3.49
Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with
probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are
worthless, but cases can only be produced in the morning before the store opens. The cost
of producing one of these is $4 while the selling price is $7. If you choose to produce 10
cases in the morning to sell, what is the probability that you will be able to meet today’s
demand?
(a)
(b)
(c)
(d)
(e)
0.20
0.30
0.40
0.10
0.90
ANSWER: e
48
Decision Analysis ● Chapter 3
3.50
Daily sales for a perishable food product are known to be 8, 9, 10, or 11 cases with
probabilities 0.2, 0.3, 0.4, and 0.1, respectively. Cases not sold during the day are
worthless, but cases can only be produced in the morning before the store opens. The cost
of producing one of these is $4 while the selling price is $7. How many cases should you
produce to maximize profit?
(a)
(b)
(c)
(d)
(e)
8
9
10
11
none of the above
ANSWER: b
3.51
Joel Turner sells donuts at the student service building. Daily sales of donuts are
approximately normally distributed with a mean of 500 and a standard deviation of 40.
Joel’s cost of purchasing each donut is 15 cents, and they are sold for 35 cents each. Joel
plans to use a marginal analysis based on the normal distribution to make a decision.
How many donuts should Joel purchase each day?
(a)
(b)
(c)
(d)
(e)
500.0
520.8
507.2
524.7
none of the above
ANSWER: c
3.52
Mickey sells newspapers on a corner every day. He pays 10 cents for each paper and sells
it for 25 cents. He knows the demand is always for 30, 40, or 50 papers, but he doesn't
know ahead of time which of these will occur. Papers left at the end of the day are sold to
a paper company for 2 cents each. If he decides to purchase 40 papers but demand is only
for 30, what would his profits be?
(a)
(b)
(c)
(d)
(e)
3.50
3.70
7.50
4.00
none of the above
ANSWER: b
49
Decision Analysis ● Chapter 3
3.53
Daily sales for submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with
probabilities of 0.2, 0.3, 0.4, and 0.1, respectively. Sandwiches not sold during the day
are worthless, and sandwiches can only be produced in the morning before the store
opens. The cost of producing one sandwich is $2, while the selling price is $3.50. If you
wish to maximize expected profit, how many sandwiches should be produced each day?
(a)
(b)
(c)
(d)
(e)
31
30
29
28
none of the above
ANSWER: c
3.54
Daily sales for submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with
probabilities of 0.2, 0.3, 0.4, and 0.1, respectively. Sandwiches not sold during the day
are worthless, and sandwiches can only be produced in the morning before the store
opens. The cost of producing one sandwich is $2, while the selling price is $3.50. If you
choose to produce 29 sandwiches in the morning to sell, what is the probability that you
will have sandwiches left over when the store closes?
(a)
(b)
(c)
(d)
(e)
0.20
0.30
0.40
0.50
0.90
ANSWER: a
3.55
Daily sales of submarine sandwiches are known to be 28, 29, 30, or 31 sandwiches with
probabilities of 0.1, 0.3, 0.4, and 0.2, respectively. The cost of producing one sandwich is
$2, while the selling price is $3.50. Sandwiches not sold during the day are given to a
local homeless shelter, and you believe that you will receive $0.40 in "goodwill" for each
sandwich given to the shelter. Sandwiches can only be produced in the morning before
the store opens. If you wish to maximize expected profit, how many sandwiches should
be produced each day?
(a)
(b)
(c)
(d)
(e)
28
29
30
31
none of the above
ANSWER: c
50
Decision Analysis ● Chapter 3
3.56
Mickey sells newspapers on a corner every day. He pays 10 cents for each paper and sells
them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he
doesn't know ahead of time which of these will occur. Papers left at the end of the day are
worthless. He purchased 40 of the papers, and at the end of the day finds that he has made
a profit of $3.50. What was demand?
(a)
(b)
(c)
(d)
(e)
30
40
50
There is insufficient information to solve this problem.
none of the above
ANSWER: a
3.57
Mickey sells newspapers on a corner every day. He pays 10 cents for each paper and sells
them for 25 cents. He knows that the demand is always for 30, 40, or 50 papers, but he
doesn't know ahead of time which of these will occur. Papers left at the end of the day are
sold to a paper company. If he decides to purchase 40 papers but demand is only for 30,
at what price must he sell the remaining papers to the paper company to earn a profit of
$3.70?
(a)
(b)
(c)
(d)
(e)
$0.05
$0.04
$0.03
$0.02
none of the above
ANSWER: d
3.58
Katie Hammond is paying her way through college by working at various odd jobs. She
contracted with the school to produce and sell programs at football games. The cost of
producing the programs is 50 cents each and they sell for $1.25 each. Programs not sold
at the game are worthless. Demand for programs at each game is normally distributed
with a mean of 2,500 and a standard deviation of 200. How many should Katie produce
for the upcoming game (round off to the nearest unit)?
(a)
(b)
(c)
(d)
(e)
2,550
2,580
2,500
2,700
none of the above
ANSWER: a
51
Decision Analysis ● Chapter 3
3.59
J. Tom Ball has developed plans for a therapy clinic for stressed-out chemical plant
workers. He has estimated that demand for services (measured in hours) will be normally
distributed with a mean of 120 hours (per month) and a standard deviation of 20. J. Tom
foresees fixed monthly expenses of $3,000. He plans to contract the work to unemployed
Ph.D.s in psychology. He will pay them $50 per hour for their time, and this is his
variable cost of providing service. He will charge $80 per hour to his clients. If J. Tom
is to break even on this venture, how many hours per month of therapy time must be
demanded?
(a)
(b)
(c)
(d)
(e)
100
600
1,200
60
none of the above
ANSWER: a
3.60
J. Tom Ball has developed plans for a therapy clinic for stressed-out chemical plant
workers. He has estimated that demand for services (measured in hours) will be normally
distributed with a mean of 120 hours (per month) and a standard deviation of 20. J. Tom
foresees fixed monthly expenses of $3,000. He will charge $80 per hour to his clients. He
plans to contract the work to unemployed Ph.D.s in psychology. What must he pay them
per hour if he wants the break-even point to be 100 hours per month?
(a)
(b)
(c)
(d)
(e)
$40/hr
$50/hr
$60/hr
$70/hr
none of the above
ANSWER: b
3.61
Decision trees are particularly useful when
(a)
(b)
(c)
(d)
(e)
perfect information is available.
formulating a conditional values table.
the opportunity loss table is available.
a sequence of decisions must be made.
all possible outcomes and alternatives are not known.
ANSWER: d
3.62
The expected value of sample information (EVSI) can be used to
(a)
(b)
(c)
(d)
(e)
establish a maximum amount to spend on additional information.
calculate conditional probabilities.
establish risk avoidance.
provide points on a utility curve.
none of the above
ANSWER: a
52
Decision Analysis ● Chapter 3
3.63
A market research survey is available for $10,000. Using a decision tree analysis, it is
found that the expected monetary value with no survey is $62,000. If the expected value
of sample information is -$7,000, what is the expected monetary value with the survey?
(a)
(b)
(c)
(d)
(e)
$45,000
$62,000
-$17,000
$55,000
none of the above
ANSWER: a
3.64
A market research survey is available for $10,000. Using a decision tree analysis, it is
found that the expected monetary value with the survey is $75,000. The expected
monetary value with no survey is $62,000. What is the expected value of sample
information?
(a)
(b)
(c)
(d)
(e)
-$7,000
$3,000
$7,000
$13,000
none of the above
ANSWER: d
3.65
Bayes’ Theorem enables decision makers to revise probabilities based on
(a) perfect information.
(b) knowing, ahead of time, the actual outcome of the decision.
(c) additional information.
(d) measurements of utility.
(e) none of the above
ANSWER: c
3.66
A company is considering producing a new children’s bar soap. A market research firm
has told the company that if they perform a survey the successful production of a
favorable market occurs 65 percent of the time. That is, P(positive survey│favorable
market) = 0.65. Similarly, 40 percent of the time the survey falsely predicts a favorable
market; thus, P(positive survey│unfavorable market) = 0.40. These statistics indicate the
accuracy of the survey. Prior to contacting the market research firm, the company’s best
estimate of a favorable market was 50 percent. So, P(favorable market) = 0.50 and
P(unfavorable market) = 0.50. Using Bayes’ theorem, determine the probability of a
favorable market given a favorable survey.
(a) 0.62
(b) 0.38
(c) 0.53
(d) 0.65
(e) none of the above
ANSWER: a
53
Decision Analysis ● Chapter 3
3.67
The following table provides information regarding probabilities for survey results for two
states of nature.
Survey
Results
Positive
Negative
Favorable Market
(FM)
0.65
0.35
Unfavorable Market
(UM)
0.40
0.60
(e.g., P(positive survey|FM)=0.65; P(positive survey|UM)=0.40)
The prior probability of a favorable market is 0.70, and an unfavorable market 0.30.
Determine the probability that the survey will predict a favorable market.
(a)
(b)
(c)
(d)
(e)
0.65
0.40
0.575
0.657
none of the above
ANSWER: c
3.68
The following table provides information regarding probabilities for survey results for two
states of nature.
Survey
Results
Positive
Negative
Favorable Market
(FM)
0.65
0.35
Unfavorable Market
(UM)
0.40
0.60
(e.g., P(positive survey|FM)=0.65; P(positive survey|UM)=0.40)
What is the probability that if a favorable market occurs, the survey will have been
positive?
(a)
(b)
(c)
(d)
(e)
0.40
0.65
0.35
0.60
none of the above
ANSWER: b
54
Decision Analysis ● Chapter 3
3.69
Utilization of Bayes' Theorem requires the use of all but
(a)
(b)
(c)
(d)
(e)
prior probabilities.
marginal probabilities.
conditional probabilities.
posterior probabilities.
expected monetary values (EMV).
ANSWER: e
3.70
A risk avoider is a person for whom the utility of an outcome
(a)
(b)
(c)
(d)
(e)
decreases as the monetary value increases.
stays the same as monetary value increases.
increases as the monetary value increases.
increases at a decreasing rate as monetary value increases.
none of the above
ANSWER: d
3.71
A utility curve showing utility increasing at an increasing rate as the monetary value
increases represents
(a)
(b)
(c)
(d)
(e)
a risk avoider.
utility assessment.
a risk seeker.
conditional values.
expected utilities.
ANSWER: c
3.72
In constructing a utility curve,
(a) a comparison is made with the different amounts of money at different times.
(b) the certainty of a certain amount is compared with the willingness to gamble that
amount on a larger amount.
(c) one takes the risk out of gambling.
(d) inflation plays a critical part in the evaluation.
(e) none of the above
ANSWER: b
3.73
Utility values range from
(a) -1 to 1
(b) 1 to 10
(c) 0 to 1
(d) 1 to 100
(e) none of the above
ANSWER: c
55
Decision Analysis ● Chapter 3
3.74
A rational decision maker must choose between two alternatives. Alternative 1 has a
higher EMV than Alternative 2, but the decision maker chooses Alternative 2. What
might explain why this occurs?
(a)
(b)
(c)
(d)
(e)
Alternative 2 may have a higher expected utility.
Alternative 1 may have a lower expected opportunity loss.
The probabilities are not known.
A rational decision maker could not possibly choose alternative 2.
none of the above
ANSWER: a
3.75
Robert Weed is considering purchasing life insurance. He must pay a $180 premium for a
$100,000 life insurance policy. If he dies this year, his beneficiary will receive $100,000.
If he does not die this year, the insurance company pays nothing and Robert must consider
paying another premium next year. Based on actuarial tables, there is a 0.001 probability
that Robert will die this year. If Robert wishes to maximize his EMV, he would not buy
the policy if the EMV were negative for him. He has determined that the EMV is, indeed
negative for him, but decides to purchase the insurance anyway. Why?
(a) He believes that the actual likelihood of his death occurring in the next twelve
months is really much greater than the actuarial estimate.
(b) While the EMV is negative, the utility gained from purchasing the insurance is
positive, and high.
(c) Mr. Weed is not rational.
(d) (a) or (c)
(e) none of the above
ANSWER: b
3.76
If one's utility curve is not a straight line (i.e., risk indifferent), then one's utility can, over
a particular range of EMV,
(a)
(b)
(c)
(d)
(e)
increase at an increasing rate as the monetary value increases.
increase at an increasing rate as the monetary value decreases.
increase at a decreasing rate as the monetary value increases.
increase at a decreasing rate as the monetary value decreases.
any of the above
ANSWER: e
3.77
It is sometimes said that "Those who gamble the most are the ones who can least afford to
lose." These people gamble because
(a)
(b)
(c)
(d)
(e)
the EMV is positive.
the EMV is negative.
the gambler has no family to consider if he/she dies.
there is utility other than monetary to consider.
none of the above
ANSWER: d
56
Decision Analysis ● Chapter 3
PROBLEMS
3.78
A concessionaire for the local ballpark has developed a table of conditional values for the
various alternatives (stocking decision) and states of nature (size of crowd).
STATES OF NATURE
(size of crowd)
Large
Average
Small
$22,000
$12,000 - $2,000
$15,000
$12,000
$6,000
$ 9,000
$ 6,000
$5,000
Alternatives
Large Inventory
Average Inventory
Small Inventory
If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for
an average crowd, and 0.20 for a small crowd, determine:
(a) the alternative that provides the greatest expected monetary value (EMV)
(b) the expected value of perfect information (EVPI)
ANSWERS:
(a) For large inventory alternative maximum EMV = $12,200
(b) EVPI = 13800 – 12200 = 1,600
3.79
A concessionaire for the local ballpark has developed a table of conditional values for the
various alternatives (stocking decision) and states of nature (size of crowd).
Alternatives
Large Inventory
Average Inventory
Small Inventory
States of Nature
(size of crowd)
Large
Average Small
$22,000 $12,000 - $2,000
$15,000 $12,000
$6,000
$ 9,000 $ 6,000
$5,000
If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for
an average crowd, and 0.20 for a small crowd, determine:
(a) the opportunity loss table
(b) minimum expected opportunity loss (EOL)
ANSWERS:
(a) Opportunity Loss Table
Alternatives
States of Nature
Large Average Small
Large
0
Average
7,000
Small
13,000
(b) minimum EOL = $1,600
0
0
6,000
57
8,000
0
1,000
Decision Analysis ● Chapter 3
3.80
The ABC Co. is considering a new consumer product. They believe there is a probability
of 0.4 that the XYZ Co. will come out with a competitive product. If ABC adds an
assembly line for the product and XYZ does not follow with a competitive product, their
expected profit is $40,000; if they add an assembly line and XYZ does follow, they still
expect a $10,000 profit. If ABC adds a new plant addition and XYZ does not produce a
competitive product, they expect a profit of $600,000; if XYZ does compete for this
market, ABC expects a loss of $100,000.
(a)
(b)
(c)
(d)
determine the EMV of each decision
determine the EOL of each decision
compare the results of a and b
calculate the EVPI
ANSWERS:
(a)
Decision
add assembly line
plant addition
do nothing
EMV
$28,000
$320,000
$0
Decision
add assembly line
plant addition
do nothing
EOL
$336,000
$44,000
$364,000
(b)
(c) The plant addition is best for both models. The maximum EMV alternative is always
the same as the minimum EOL alternative.
(d) EVPI = 44,000
3.81
The ABC Co. is considering a new consumer product. They have no idea whether or not
the XYZ Co. will come out with a competitive product. If ABC adds an assembly line for
the product and XYZ does not follow with a competitive product, their expected profit is
$40,000; if they add an assembly line and XYZ does follow, they still expect a $10,000
profit. If ABC adds a new plant addition and XYZ does not produce a competitive
product, they expect a profit of $600,000; if XYZ does compete for this market, ABC
expects a loss of $100,000.
Calculate Hurwicz’s criterion of realism using α’s of 0.7, 0.3, and 0.1.
ANSWERS:
Decision
add assembly line
plant addition
do nothing
Criterion of Realism
α = 0.7
α = 0.3
α = 0.1
$31,000
$19,000
$13,000
$390,000 $110,000 - $30,000
$0
$0
$0
58
Decision Analysis ● Chapter 3
3.82
Barbour Electric is considering the introduction of a new product. This product can be
produced in one of several ways: (a) using the present assembly line at a cost of $25 per
unit, (b) using the current assembly line after it has been overhauled (at a cost of $10,000)
with a cost of $22 per unit; and (c) on an entirely new assembly line (costing $30,000)
designed especially for the new product with a per unit cost of $20. Barbour is worried,
however, about the impact of competition. If no competition occurs, they expect to sell
15,000 units the first year. With competition, the number of units sold is expected to drop
to 9,000. At the moment, their best estimate is that there is a 40% chance of competition.
They have decided to make their decision based on the first year sales.
(a) develop the decision table (EMV)
(b) develop a decision table (EOL)
(c) what should they do?
ANSWERS:
(a)
Alternative
(a) Present line
(b) Overhauled line
No
Competition
Competition
EMV
P = 0.60
$375,000
$340,000
P = 0.40
$225,000
$208,000
$315,000
$287,000
$330,000
$210,000
$282,000
(c) New line
(b)
Alternative
(a) Present line
(b) Overhauled line
(c) New line
No
Competition
P = 0.60
$45,000
$10,000
$0
(c) They should build the new line.
59
Competition
P = 0.40
$17,000
$0
$2,000
EMV
$33,800
$6000
$800
Decision Analysis ● Chapter 3
3.83
The following payoff table provides profits based on various possible decision alternatives
and various levels of demand.
States of Nature
Demand
Alternatives
Low Medium High
Alternative 1
80
120
140
Alternative 2
90
90
90
Alternative 3
50
70
150
The probability of a low demand is 0.4, while the probability of a medium and high
demand is each 0.3.
(a) What decision would an optimist make?
(b) What decision would a pessimist make?
(c) What is the highest possible expected monetary value?
(d) Calculate the expected value of perfect information for this situation.
ANSWER:
(a) Alternative 3
(b) Alternative 2
(c) maximum EMV = 110
(d) EVPI = 117- 110 = 7
3.84
The ABC Co. is considering a new consumer product. They believe that the XYZ Co.
may come out with a competing product. If ABC adds an assembly line for the product
and XYZ does not follow with a competitive product, their expected profit is $40,000; if
they add an assembly line and XYZ does follow, they still expect a $10,000 profit. If
ABC adds a new plant addition and XYZ does not produce a competitive product, they
expect a profit of $600,000; if XYZ does compete for this market, ABC expects a loss of
$100,000. For what value of probability that XYZ will offer a competing product will
ABC be indifferent between the alternatives?
ANSWER:
Let X = probability XYZ offers a competing product. Then:
EMV(assembly line) = $10,000*X + $40,000*(1-X)
EMV(addition) = -$100,000*X + $600,000*(1-X) or:
$10,000*X + $40,000 * (1-X) = -$100,000*X + $600,000*(1-X)
or:
$10,000*X - $40,000*X + $40,000 = -$100,000*X -$600,000*X + $600,000
-$30,000*X + $700,000 *X = $600,000 - $40,000
$670,000*X = $560,000
X = $560,000/$670,000 = 0.836
If the probability that XYZ will offer a competing product is estimated to be 0.836, then
ABC will be indifferent between the two alternatives. If the probability that XYZ will
offer a competing product is estimated to be less than 0.836, then ABC should invest in
the addition.
60
Decision Analysis ● Chapter 3
3.85
A company is considering expansion of its current facility to meet increasing demand. A
major expansion would cost $500,000, while a minor expansion would cost $200,000. If
demand is high in the future, the major expansion would result in an additional profit of
$800,000, but if demand is low, then there would be a loss of $500,000. If demand is
high, the minor expansion will result in an increase in profits of $200,000, but if demand
is low, then there is a loss of $100,000. The company has the option of not expanding.
For what probability of a high demand will the company be indifferent between the two
expansion alternatives?
ANSWER:
Alternatives
Major expansion
Minor expansion
Do nothing
States of Nature
Demand is high
Demand is low
$800,000 - $500,000 -$500,000 - $500,000
$200,000 - $200,000 -$100,000 - $200,000
$0
$0
Alternatives
Major expansion
Minor expansion
Do nothing
States of Nature
Demand is high
Demand is low
$300,000
-$1,000,000
$0
-$300,000
$0
$0
If we define X = probability of High Demand, then:
$300,000*X - $1,000,000*(1-X) = $0*X - $300,000*(1-X)
X = 0.7
For a probability of High Demand equal to 0.7, the decision maker would be indifferent
between the two expansion alternatives.
61
Decision Analysis ● Chapter 3
3.86
Orders for clothing from a particular manufacturer for this year’s Christmas shopping
season must be placed in February. The cost per unit for a particular dress is $20 while
the anticipated selling price is $50. Demand is projected to be 50, 60, or 70 units. There
is a 40 percent chance that demand will be 50 units, a 50 percent chance that demand will
be 60 units, and a 10 percent chance that demand will be 70 units. The company believes
they can sell any leftover goods to a discount store, but they are uncertain as to the price
the discount store will pay. For what price to be paid by the discount store would they
order 70 cases of dresses in February?
ANSWER:
Let X = price to be paid by the discount store; then:
Payoff Table:
Alternatives
Order 50
Order 60
Order 70
Probabilities:
States of Nature
Demand (units)
50
60
1500
1500
1300 + 10X
1800
1100 + 20X 1600 + 10X
0.4
0. 5
70
1500
1800
2100
0.1
And, the company would order 70 units when EMV(70) = EMV(60).
(1300 + 10X) *0.4 + 1800*0.5 + 1800*0.1 =
(1100+20X)*0.4 + (1600+10X)*0.5 + 2100*0.1
520+ 4X + 900 +180 = 440 + 8X +800 + 5X +210
9X = 150
X = 150/9 = 16.67
Therefore, if the company could get at least $16.67 per dress from the discount store, the
appropriate decision would be to order 70 units.
62
Decision Analysis ● Chapter 3
3.87
Norman L. Flowers holds the exclusive university contract for donut sales. The demand
(based on historical records) appears to follow the following distribution:
Daily Demand
(Dozens)
4
5
6
7
8
Probability
0.15
0.25
0.30
0.25
0.05
The cost of producing these is $1.20 per dozen while the selling price is $4.20 per dozen.
Based on a marginal analysis of this situation, how many donuts should Norman produce
each day?
ANSWER: P > 1.20/4.20 = 0.286. Therefore, Norman should produce seven dozen.
3.88
David N. Goliath is planning to open a sporting goods store. However, the initial
investment is $100,000. He currently has this money in a certificate of deposit earning 15
percent. He may leave it there if he decides not to open the store. If he opens the store
and it is successful he will generate a profit of $40,000. If it is not successful, he will lose
$80,000. What would the probability of a successful store have to be for David to prefer
this to investing in a CD?
ANSWER:
3.89
p(40000) +(1-p)-(80000) > 0.15(100000), therefore p > 0.79
You are considering adding a new food product to your store for resale. You are certain
that, in a month, minimum demand for the product will be 6 units, while maximum
demand will be 8 units. (Unfortunately, the new product has a one-month shelf life and is
considered to be waste at the end of the month.) You will pay $60/unit for this new
product while you plan to sell the product at a $40/unit profit. The estimated demand for
this new product in any given month is 6 units(p=0.1), 7 units(p=0.4), and 8 units(p=0.5).
Using EMV analysis, how many units of the new product should be purchased for resale?
ANSWER:
EMV(purchase 6 for resale) = 6(40)(0.1) + 6(40)(0.4) + 6(40)(0.5) = 240
EMV(purchase 7 for resale) = [6(40)-60](0.1) + 7(40)(0.4) + 7(40)(0.5) = 270
EMV(purchase 8 for resale) = [6(40)-2(60)](0.1) + [7(40)-60](0.4) + 8(40)(0.5) = 260
Choose to purchase seven units for resale (largest EMV)
63
Decision Analysis ● Chapter 3
3.90
Mark M. Upp has just been fired as the university bookstore manager for setting prices too
low (only 20 percent above suggested retail). He is considering opening a competing
bookstore near the campus, and he has begun an analysis of the situation. There are two
possible sites under consideration. One is relatively small, while the other is large. If he
opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is
low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a
profit of $80,000, but he will lose $30,000 if demand is low. He also has the option of not
opening at either site. He believes that there is a 50 percent chance that demand will be
high. A market research study will cost $5,000. The probability of a good demand given
a favorable study is 0.8. The probability of a good demand given an unfavorable study is
0.1. There is a 60 percent chance that the study will be favorable.
(a) Should Mark use the study? Why?
(b) If the study is done and the results are favorable, what would Mark's expected profit
be?
ANSWER:
(a) Yes, he should use the study. His EMV with the study is $29,800 while the highest
EMV without the study is $25,000.
(b) Given a favorable survey result, Mark would select Site 2 and have an EMV of
$53,000.
3.91
Mark M. Upp has just been fired as the university bookstore manager for setting prices too
low (only 20 percent above suggested retail). He is considering opening a competing
bookstore near the campus, and he has begun an analysis of the situation. There are two
possible sites under consideration. One is relatively small, while the other is large. If he
opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is
low, he will lose $10,000. If he opens at Site 2 and demand is high, he will generate a
profit of $80,000, but he will lose $30,000 if demand is low. He also has the option of not
opening either. He believes that there is a 50 percent chance that demand will be high.
Mark can purchase a market research study. The probability of a good demand given a
favorable study is 0.8. The probability of a good demand given an unfavorable study is
0.1. There is a 60 percent chance that the study will be favorable. Should Mark use the
study? Why? What is the maximum amount Mark should be willing to pay for this study?
What is the maximum amount he should pay for any study?
ANSWER:
Yes, he should use the study. His EMV with the study is $34,800 while the highest EMV
without the study is $25,000. He should pay no more than $9,800 for this study. He
should pay no more than $10,000 for a "perfect" study.
64
Decision Analysis ● Chapter 3
3.92
Before a marketing research study was done, John Colorado believed there was a 50/50
chance that his music store would be a success. The research team determined that there
is a 0.9 probability that the marketing research will be favorable given a successful music
store. There is also a 0.8 probability that the marketing research will be unfavorable given
an unsuccessful music store.
(a) If the marketing research is favorable, what is the revised probability of a successful
music store?
(b) If the marketing research is unfavorable, what is the revised probability of a
successful music store?
ANSWER:
(a) 0.82
(b) 0.11
3.93
Before a market survey is done, there is a 50/50 chance that a new soccer supply store
would be a success. The people doing the survey have determined that there is a 0.8
probability that the survey will be favorable given a successful store. There is also a 0.7
probability that the survey will be unfavorable given an unsuccessful store. What is the
probability that the survey will be unfavorable?
ANSWER: 0.45
3.94
Before a marketing research study was done, John Colorado believed there was a 50/50
chance that his music store would be a success. The research team determined that there
is a 0.9 probability that the marketing research will be favorable given a successful music
store. There is also a 0.8 probability that the marketing research will be unfavorable given
an unsuccessful music store.
(a) If the marketing research is favorable, what is the revised probability of an
unsuccessful music store?
(b) If the marketing research is unfavorable, what is the revised probability of an
unsuccessful music store?
ANSWER:
(a) 0.18
(b) 0.89
65
Decision Analysis ● Chapter 3
3.95
Mark M. Upp has just been fired as the university bookstore manager for setting prices too
low (only 20 percent above suggested retail). He is considering opening a competing
bookstore near the campus, and he has begun an analysis of the situation. There are two
possible sites under consideration. One is relatively small while the other is large. If he
opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is
low, he will lose $10,000. If he opens at Site 2 and demand is high he will generate a
profit of $80,000, but he will lose $30,000 if demand is low. He also has decided that he
will open at one of these sites. He believes that there is a 50 percent chance that demand
will be high. He assigns the following utilities to the different profits:
U(50,000) = 0.72
U(80,000) = 1
U(-10,000) = 0.22
U(-30,000) = 0
Using expected utility theory, what should Mark do?
ANSWER:
Expected utility (Site 1) = 0.5(0.72) + 0.5(0.22) = 0.47
Expected utility (Site 2) = 0.5(1.00) + 0.5(0.00) = 0.50
Therefore he should open at Site 2.
3.96
Mark M. Upp has just been fired as the university book store manager for setting prices
too low (only 20 percent above suggested retail). He is considering opening a competing
bookstore near the campus, and he has begun an analysis of the situation. There are two
possible sites under consideration. One is relatively small, while the other is large. If he
opens at Site 1 and demand is good, he will generate a profit of $50,000. If demand is
low, he will lose $10,000. If he opens at Site 2 and demand is high he will generate a
profit of $80,000, but he will lose $30,000 if demand is low. He also has decided that he
will open at one of these sites. He believes that there is a 50 percent chance that demand
will be high. He assigns the following utilities to the different profits:
U(50000) = ?
U(80000) = 1
U(-10000) = 0.22
U(-30000) = 0
For what value of utility for $50,000, U(50000), will Mark be indifferent between the two
alternatives?
ANSWER:
Expected utility (Site 1) = 0.5X + 0.5(0.22)
Expected utility (Site 2) = 0.5(1) + 0.5(0) = 0.50
Therefore: 0.5X + 0.5(0.22) = 0.50
or: 0.5X = 0.50 - 0.11 = 0.39
And: X = 0.39/0.5 = 0.78
Therefore, if Mark has U(50,000) = 0.78 he will be indifferent between the two
alternatives.
66
Decision Analysis ● Chapter 3
3.97
Pat Lucky would like a utility curve constructed for his monetary preference from $0 to
$10,000. Pat is willing to risk a sure $7,000 on a 50/50 chance of making $10,000 or
losing all his money. Similarly, Pat would be willing to risk a sure $5000 for a 40 percent
chance of making $10,000 (60 percent chance of losing it all). Finally, he would be
willing to risk $3,000 on a 10 percent chance of making $10,000 (90 percent chance of
losing it all). Pat also plays dogs, ponies, and state lotteries – he received a severe
concussion when dropped on his head when young. Is Pat a risk avoider or risk seeker?
ANSWER: Pat is a risk avoider.
SHORT ANSWER/ESSAY
3.98
Briefly describe decision making under certainty.
ANSWER: decision making with certain knowledge of the consequence of every
outcome
3.99
Briefly describe decision making under risk.
ANSWER: decision making with knowledge of the probability of occurrence of every
outcome
3.100 Biefly describe decision making under uncertainty.
ANSWER: decision making without knowledge of the probability of occurrence of every
outcome
3.101 In general terms, describe a decision node.
ANSWER: a node from which one of several alternatives may be chosen
3.102 In general terms, describe a state of nature node.
ANSWER: a node out of which one state will occur
3.103 Briefly describe decision tree analysis.
ANSWER: define the problem, draw the tree, assign the probabilities to the states of
nature, estimate payoffs for each alternative, compute EMV
3.104 Briefly describe EVSI.
ANSWER: EVSI = EV (best decision with sample information) – EV (of best decision
without sample information)
3.105 Describe the utility curve of a risk seeker.
ANSWER: utility increasing at an increasing rate as the monetary value increases
67
Decision Analysis ● Chapter 3
3.106 Describe the utility curve of a risk avoider.
ANSWER: utility increasing at a decreasing rate as the monetary value increases
3.107 Describe utility assessment.
ANSWER: Assign the worst outcome a utility of 0 and the best outcome a utility of 1.
Assign all other outcomes a utility value other than the best or worst outcome.
68